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String theory is the most widely accepted model for quantum gravity and as such it should give an answer to the fundamental question: what is the nature of quantum space-time? A handle on this question was provided through two of the recent conceptual advances in string theory, the (BFSS-type) matrix models and AdS/CFT duality. In my talk I'll focus on the second and discuss two places where the Ads/CFT duality has shed light on the question posed in describe the DLCQ of strings on the AdS geometry, the tiny gravitation matrix theory, according to which the quantum structure of the $AdS_{5}\times S^{5}$ geometrycontains two noncommutative fuzzy three spheres as well as a noncommutative Moyal plane. We'll argue that the appearance of noncommutative geometries is a generic feature of these matrix theories.
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